Dallas acquired the 23-year-old Connauton from Vancouver in an April trade that sent Derek Roy to the Canucks.
The first year of the contract announced Thursday is a two-way deal, meaning Connauton will make $100,000 if he plays in the minors and $600,000 if he is in the NHL. The final two years are guaranteed, $650,000 for the 2014-15 season and $800,000 for 2015-16.
Connauton played in 69 games for Chicago and Texas of the AHL last season, and had nine goals, 22 assists and 73 penalty minutes. He played in the AHL All-Star game and registered the hardest shot in a skills competition.